The molecular reduction of the vapor pressure K of a solution, that is to say, the relative reduction of pressure produced by 1 molecule of a substance held in 100 grams of a volatile liquid, can be calculated by means of the following formula:
K = (f - f')/(fP) x Min which f is the vapor pressure of the pure solvent, f' the vapor pressure of the solution, M the molecular weight of the dissolved substance, P the weight of this substance in solution in 100 grams of the solvent; if it is admitted that the relative reduction of pressure (f - f')/f is proportional to the concentration. As this proportionality is rarely rigorous, even when the solutions are very dilute, I have been obliged in these comparative studies to use solutions which always have nearly the same molecular concentrations and contain four to five molecules of substance held per 100 molecules of volatile solvent. A greater dilution would not allow sufficiently exact measurements. All the experiments were performed by the barometric method and conducted like those I have run in ether solutions (Comptes rendus of 16 December 1886). The tubes were plunged in a water bath limited by parallel glasses, constantly agitated, and heated at will.
In each case the temperature was so chosen that the vapor pressure of the pure solvent was about 40 millimeters of mercury. The measurements were made from fifteen to forty-five minutes after agitation of the contents of each tube, the temperature being constant.
I have used 12 different volatile liquids as solvents, namely, water, phosphorous chloride, the sulfide of carbon, the bichloride of carbon (CCl4), chloroform, amylene, benzene, methyl iodide, ethyl bromide, ordinary ether, acetone, methyl alcohol.
In water I have dissolved the following organic materials: cane sugar, glucose, tartaric acid, citric acid, urea. All these substances have produced sensibly the same molecular reduction in vapor pressure: K = 0.185. I have, for the present, left the mineral substances to one side; actually, the effect of these substances has been determined by enough conclusive experiments performed by Wüllner (Pogg. Ann., vol. 103-110, 1858-1860), by me (Comptes rendus, 87, 1878), and recently by M. Tammann (Wiedemann Ann. 24, 1885).
In solvents other than water, I have dissolved materials as little volatile as possible, chosen among the following: oil of turpentine, naphthalene, anthracene, sesquichloride of carbon (C2Cl6), methyl salicylate, ethyl benzoate, antimonous chloride, mercury ethyl, benzoic, valeric, and trichloroacetic acids, thymol, nitrobenzene, and aniline. The error due to the vapor pressure of these compounds can often be rendered negligible. The vapor pressure of the dissolved substances is, in fact, considerably reduced by their mixture with a great excess of the solvent; and in order that it should not exercise a sensible influence on the results, it is enough that it should not surpass 5 or 6 millimeters at the experimental temperature.
The molecular reductions in vapor pressure caused by these different bodies in the same solvent are constantly grouped around two values, of which one, which I call normal, is double the other. The normal reduction is always produced by simple and chlorinated hydrocarbons and by ethers; the anomalous reduction is almost always produced by acids. There are found, however, solvents in which all the dissolved bodies produce the same molecular reduction of pressure; such are, for example, ether (loc. cit.) and acetone.
Among the volatile solvents examined there are two, water and benzene, in which I have studied carefully the lowering of the freezing point (Comptes rendus vol. 95-101; and Annales de Chimie et de Physique, 5th series, vol. 28 and 6th series, vol. 2 and 8). The comparison of the results obtained shows that for all solutions made in the same solvent there is a nearly constant relation between the molecular lowering of freezing point and the molecular reduction of vapor pressure. In water this ratio is equal to 100; in benzene it is equal to 60, nearly 1/20.
If we divide the molecular reduction of vapor pressure K produced in a determined volatile liquid by the molecular weight M' of the liquid, the quotient obtained K/M' represents the relative reduction of pressure which will be produced by 1 molecule of substance held in 100 molecules of volatile solvent. In making this calculation for the normal values of K produced in the various solvents by the organic materials and nonsaline metallic compounds, I have obtained these results:
| Solvent | Molecular weight of solvent M' | Normal molecular reduction of pressure K | Reduction of pressure produced by 1 mol. in 100 mols. K/M' |
| Water | 18 | 0.185 | 0.0102 |
| Phosphorus chloride | 137.5 | 1.49 | 0.0108 |
| Sulfide of carbon | 76 | 0.80 | 0.0105 |
| Bichloride of carbon (CCl4) | 154 | 1.62 | 0.0105 |
| Chloroform | 119.5 | 1.30 | 0.0109 |
| Amylene | 70 | 0.74 | 0.0106 |
| Benzene | 78 | 0.83 | 0.0106 |
| Methyl iodide | 142 | 1.49 | 0.0105 |
| Ethyl bromide | 109 | 1.18 | 0.0109 |
| Ether | 74 | 0.71 | 0.0096 |
| Acetone | 58 | 0.59 | 0.0101 |
| Methyl alcohol | 32 | 0.33 | 0.0103 |
The values of K and M' assigned in the table vary in the ratio from 1 to 9; in spite of this, the values of K/M' vary very little and remain always near the mean 0.0105. We can then say,
1 molecule of nonsaline substance (held in the solvent) dissolved in 100 molecules of any volatile liquid decreases the vapor pressure of this liquid by a nearly constant fraction, nearly 0.0105.
This law is entirely analogous to that which I announced in 1882 relating to the lowering of the freezing point of solvents. The anomalies which it presents are explained for the most part by admitting that, in certain liquids, the dissolved molecules can be formed from two chemical molecules.
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